Problem: Simplify the following expression: $\sqrt{18}-\sqrt{8}+\sqrt{50}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{18}-\sqrt{8}+\sqrt{50}$ $= \sqrt{9 \cdot 2}-\sqrt{4 \cdot 2}+\sqrt{25 \cdot 2}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{2}-\sqrt{4} \cdot \sqrt{2}+\sqrt{25} \cdot \sqrt{2}$ $= 3\sqrt{2}-2\sqrt{2}+5\sqrt{2}$ Finally, simplify by combining the terms. $= ( 3 - 2 + 5 )\sqrt{2} = 6\sqrt{2}$